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IRBM 34 (2013) 349–356
Research in Imaging and Health Technologies
3D articulated growth model of the fetus skeleton, envelope and soft tissues
A. Serrurier a , S. Dahdouh a,∗ , G. Captier c , V. Calmels b , C. Adamsbaum a,b,d , I. Bloch a
a
Institut Mines-Telecom, Telecom ParisTech/CNRS LTCI/Whist Lab, 46, rue Barrault, 75013 Paris, France
b General and Pediatric Radiology Departments, Bicêtre Hospital, AP–HP, Paris, France
c Anatomy laboratory, Montpellier-1 University, Montpellier, France
d Paris-Sud University, 91405 Orsay cedex, France
Received 13 May 2013; received in revised form 3 June 2013; accepted 28 June 2013
Available online 23 September 2013
Abstract
Fetal dosimetry studies require the development of accurate 3D models of the fetus. This paper proposes a 3D articulated fetal growth model
including skeleton, body envelope, brain and lungs based on medical images of ten different fetuses acquired in clinical routine. The structures of
interest were semi-manually segmented from the images and surface meshes were generated. A generic mesh of each structure has been deformed
towards the segmented ones. By interpolating linearly between the subjects of the database, each structure can be estimated at any age and in any
position. This process results in an automated model, the operator being only required to specify the age and position of the desired estimated fetus.
© 2013 Elsevier Masson SAS. All rights reserved.
1. Introduction
In order to assess the impact of radiofrequency waves on
human beings, dosimetry studies have to be performed. To do so,
reliable human models have to be constructed. While many adult
models have been developed, only few studies have focused on
embryo [1] and fetus [2]. To our knowledge, no in silico model
of fetus growth has been proposed in the literature. Our objective
in this paper is thus to develop a three-dimensional (3D) growth
model of the fetus including fetal skeleton, body envelope, brain
and lungs. It aims at estimating fetuses at any age and position
from 14 to 32 weeks of amenorrhea (WA). Beyond the scope
of dosimetry, such a model will also be useful in fields like
developmental studies, medical research, teaching or surgery
simulations. The construction of the model and a few selected
results are presented in this paper.
2. Material and methods
2.1. Data
Several sets of medical images of various modalities representing different fetuses were used for this project, as
∗
Corresponding author.
E-mail address: [email protected] (S. Dahdouh).
1959-0318/$ – see front matter © 2013 Elsevier Masson SAS. All rights reserved.
http://dx.doi.org/10.1016/j.irbm.2013.06.002
summarized in Table 1. Using complementary 3D imaging
modalities allows us to cover a large range of ages and visible structures. All the images were recorded on pregnant women
during medical examinations except two sets of micro-Computer
Tomography (μCT) recorded on fetuses conserved in formalin
for several decades.
2.2. Algorithm
In order to construct a 3D articulated growth model from these
data, a multi-steps algorithm has been developed as shown in
Fig. 1. First, a semi-manual strategy is applied in order to obtain
reliable 3D meshes from medical imaging data. These meshes
are then used to construct a growth evolution model of the fetal
body throughout pregnancy. The whole method is detailed in the
following sections.
2.2.1. Image-based 3D meshes construction
Different image processing strategies have been used in
order to retrieve the structures of interest according to data
type. For Magnetic Resonance Imaging (MRI) data, brain and
lungs have been segmented using the method presented in
Anquez et al. [3], while in 3D Ultrasound (US) segmentation
has been performed manually due to the very low signal to
noise ratio. Semi-automatic segmentation procedures have been
used for the skeleton and envelope segmentation on CT-scan and
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Table 1
Data characteristics.
Modality
Pregnancy stage(WA)
Slice thickness(mm)
Image resolution(mm/px)
Subject
Structures of interest
CT
CT
μCT
μCT
MRI
MRI
MRI
MRI
MRI
3D US
27
32
14
16
20
26
30
32
34.5
13
1.2
1
0.048
0.144
0.74
1.6
4
4
4
7.6
0.64
0.96
0.036
0.036
0.74
1.36
0.94
0.94
0.94
0.76
In vivo
In vivo
Formalin
Formalin
In vivo
In vivo
In vivo
In vivo
In vivo
In vivo
Skeleton
Skeleton + envelope
Skeleton + lungs + brain
Skeleton
Brain
Brain + lungs
Brain + lungs
Brain + lungs
Brain + lungs
Brain + lungs
Fig. 1. Global algorithm.
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351
Fig. 2. Semi-manually segmented skeletons from the database.
μ-CT data on which a pre-processing step aiming at enhancing
structures contrast and reducing high frequency noise has been
applied. A surface triangular mesh has been generated for each
structure.
Examples of these semi-manual segmentations can be seen
in Fig. 2 where four fetal skeletons at different ages have been
segmented.
This process resulted in a database of meshed structures
defined as follows: the brain, referring to the addition of the
brain and the cerebrospinal fluid, the lungs, viewed as a unique
structure composed of two separated parts, and the skeleton,
split into 14 substructures within which no relative displacement
between the bones is allowed in our model, more specifically:
• the head;
• the trunk and the pelvis together, including the pelvis bones,
the spine, the ribs, the clavicles and the scapulas;
• each of the two humerus;
• each of the two forearms;
• each of the two hands;
• each of the two femurs;
• each of the two legs;
• each of the two feet.
2.2.2. Generic modeling
2.2.2.1. Topology unification. In order to be able to perform
an interpolation between the different meshes of the database,
one needs a similar topology for the meshes of equivalent structures at each age. Thus, a generic mesh has been chosen as
reference for each structure. The meshes derived from the CT
data at 32 WA for the skeleton sections, being more precise
and of higher quality than the others, have been chosen. For
similar reasons, brain and lungs from the MRI images at 34.5
WA were used. For each structure, the chosen generic mesh has
been deformed towards the equivalent mesh at each age using a
set of manually and automatically selected landmarks on both
meshes. For soft tissues, a deformation based on a 3D deformation method based on the 3D Moving Least Square (MLS) [4]
has been performed whereas for some of the skeleton structures,
this operation has been preceded by a 3D Kriging [5] one using
the same landmarks.
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Fig. 3. Fetus skulls at different ages with their local coordinate system and superposition of these skulls in the same local coordinate system.
The deformed meshes have finally been substituted to the
original ones for the rest of the study, providing for each structure
a mesh of same topology at all ages.
2.2.2.2. Structures alignment and interpolation. In order to
align the structure meshes at different ages, a local coordinate system has been defined for each of the skeleton sections
and each of the soft tissues based on anatomic and geometric
considerations.
An example is shown in Fig. 3, where anatomic characteristics such as ocular globes are used to define a local coordinate
system which allows the superposition of the same structure at
all ages.
By placing each structure mesh in its local coordinate system, an estimation of the structure shapes at any age using a
linear interpolation between the vertices of the meshes is made
possible. Since, except for the 14 WA fetus, key ages (e.g the
ones where real data are available) for skeleton and soft tissues
Fig. 4. Envelope decompositions.
Fig. 5. Rough envelope obtained after Algorithm 2 and zoom on remaining articulation problems.
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Fig. 6. Resulting envelope obtained after Algorithm 3.
Fig. 7. Three 3D meshes of reference segmented fetuses (top) and their simulated counterparts with our model (bottom).
are not the same, the Algorithm 1 has been applied prior to the
interpolation step.
2.2.2.3. Skeleton reconstruction. The various estimated skeleton section meshes are then assembled together to form a
fetus in the desired position, the articulations between the
skeleton sections being derived from the observed articulations
of the fetuses of the database using geometrical considerations.
2.2.2.4. Soft tissues positioning. The estimated soft tissues
meshes are finally positioned in relation to their underlying
skeleton structures, i.e. the head for the brain, and the spine
and rib cage for the lungs, the insertion conflicts being avoided
thanks to Algorithm 1.
Algorithm 1 (Meshes reshaping).
Data: Soft tissues, Skeleton, Soft tissues key ages, Skeleton key ages
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Fig. 8. 3D meshes of fetuses with the same position at different ages.
Result: Soft tissues, Skeleton
foreach Age do
if Age ∈ Soft tissues key ages then
Rescale skeleton structure according to soft tissue
end
if Age ∈ Skeleton key ages then
Rescale soft tissue according to skeleton
end
end
2.2.2.5. Envelope reconstruction. Since the fetal envelope
varies according to the age of the fetus but also, unlike the
above structures, according to the desired position of the fetus
regardless of its age, a different strategy has to be developed. We decided therefore to use a single generic envelop
mesh (the one corresonding to the 32 WA fetus) deformed
towards the desired fetus according to the underlying skeleton.
The generic envelope Env is first split into 14 sub-envelopes
Env(i) corresponding to the skeletal structures Sk(i)i ∈ {1..14}
described in the previous sections. Each sub-envelope is then
split into two parts: the inner envelope in Env(i) corresponding
to the middle part of the sub-envelope, and the outer envelope
out Env(i) corresponding to the parts used as jonctions with the
other limbs, as shown in Fig. 4.
The generic envelope Env is then deformed using a two
step algorithm. The first step ensures the production of a first
rough approximation of the envelope, as explained in Algorithm
2.
Algorithm 2 (First step).
Data: m Sk(i)i ∈ {1..14} : Sk (i) of the generic skeleton,
d Sk(i)i ∈ {1..14} : Sk (i) of the target skeleton, Env(i)
Result: r in Env(i), r out Env(i), i in {1..14}
foreach Sk(i)i ∈ {1..14} do
m points ← Select 500 random vertices on m Sk(i)
d points ← Get equivalent vertices on d Sk(i)
res Env(i) ← Deform Env(i) using m points and d points in a
MLS procedure using the Euclidean distance and a mild rigidity
factor
res Env (i) = r in Env(i) ∪ r out Env(i)
end
As we can see in Fig. 5, the method’s result gives a global
idea of the final envelope but in some cases, body articulations
are shrinked and twisted whereas in other cases they seem to be
separated from the rest of the body.
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Fig. 9. Means of left and right values for the length of different fetus limbs (femur, tibia, humerus, radius) in relation to fetus ages (red) superimposed on charts
values. In each case, the mean chart value as well as the confidence interval defined by the 3rd and 97th centile are also drawn.
In order to address these issues, the outcome of Algorithm
2 is used as a guideline to perform a second deformation of
Env, handling specifically the articulation problems. The idea
consists in constraining strongly the inner envelopes vertices to
fit the outcome of Algorithm 2 while relaxing the outer envelope
vertices to ensure smooth articulations, as detailed in Algorithm
3. As we can see in Fig. 6, body articulations are now correctly
represented and the result seems visually coherent.
Algorithm 3 (Second step).
Data: in Env(i), r in Env(i), Env
Result: res Env
foreach in Env(i) do
m points ← Select 2000 random vertices on in Env(i)
d points ← Get equivalent vertices on r in Env(i)
res Env ← Deform Env using m points and d points in a
MLS procedure using a topological distance and a strong rigidity
factor.
end
3. Results
In order to assess the validity of our model, some qualitative
and quantitative experiments have been performed.
3.1. Qualitative validation
Two experiments have been carried out to evaluate the
model’s behavior with respect to age and position criteria.
Fig. 10. Bi-parietal diameter of our model in relation to fetus age (red) superimposed on charts values.
First, fetuses at three different ages have been generated and
positioned in the same position as reference fetuses taken from
the FEMONUM database,1 as illustrated in Fig. 7. Because the
inter-subject variability is not modeled, an exact registration is
impossible. Thus, the estimated and reference fetuses have been
compared in terms of global shape appearance and soft tissues
positioning. Our model seems able to reproduce a real fetus
position with its global dimensions and soft tissue positioning
preserved. However, since our model articulations do not have
1
http://femonum.telecom-paristech.fr/.
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all the freedom degrees that exist in real ones, some positions
(like the 26 WA one) could not be reached exactly.
In a second experiment, fetuses with the same position but at
different ages have been generated, as illustrated in Fig. 8. Since
no mobility degree has been allowed for the spine, it reflects the
shape of the fetuses present in the database and the positions
at 14 and 32 WA are slightly different, the one at 32 weeks
being more curled up. Despite this limitation, the global position
is preserved, the soft tissues are well positioned, and the fetal
proportions are respected.
3.2. Quantitative validation
In order to assess the validity of the modeled skeletons, some
fetal biometry markers have been computed and compared to
the literature [6] and to the charts from the French college of
fetal ultrasound imaging [7]. The results are given in Fig. 9. As
we can see, the values representing the modeled fetus are of the
same order as the mean value and are always inside the confidence interval, which seems to validate the proposed approach
for skeletal evolution regarding to limbs.
The same comparison is made for the bi-parietal diameter,
commonly used in pregnancy follow-up as shown in Fig. 10. As
we can see here, the computed values are still within the confidence interval. However, in some cases, the values are closer to
the extremities of the interval than to the mean curve. These cases
correspond to the ages where information was given either for
the soft-tissues or for the skeleton. At these key ages, the model
reflects exactly the data and thus the fact that our model does
not take into account intra-ages variability.
4. Discussion and conclusion
In this paper, a growth model allowing the construction of a
fetus at any age between 14 and 32 WA and placed in any position
has been presented. This process ensures a realistic model but
raises also a few limitations due to the heavy processing involved
with medical images. The model relies indeed on a limited
number of subjects not allowing us to take into account the variability between fetuses of a same age. This induces a bias in
the evolution model since inter-individual variability cannot be
stretched apart from inter-ages variability. The behavior of the
model regarding age and position has been studied and comparisons have been performed with classical charts values. Despite
the modest size of the initial database, these two validations
have shown that the modeled fetuses fit in terms of biometry
measures and visual appearance to real ones. Increasing the
size of the image database will naturally improve this fitting
and allow even more realistic models. The presented modeling
should be used in a near future for dosimetry studies on the
fetus.
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